Non-classical/Exponential Decay Regimes in Multiscale Generated Isotropic Turbulence

Abstract

The effects of time-lasting initial production mechanisms in homogeneous isotropic turbulence (HIT) decay are here investigated by the use of an eddy-damped quasi-normal Markovian (EDQNM) model. The statistical properties of these effects are included in the EDQNM model by the use of an ad-hoc term which mimics the turbulent energy production in grid turbulence experiments. This new version of the EDQNM model has been recently proposed by Meldi et al. (J Fluid Mech 756:816–843, 2014). The sensitivity to the two model parameters β and α has been investigated. The parameters determine the shape of the forcing term in the spectral domain and its time evolution, respectively.

The results indicate that the shape of the energy spectrum in the forced range is sensitive to the parameter β, while this parameter has a weak global effect on the main HIT statistics ($\mathcal{K}$, L, …).

The observation of the sensitivity of the physical quantities to the parameter α allowed for the identification of three main classes. For α ≫ 1, the forcing F(k, t) decays faster than the physical dissipation rate ɛ. A classical power law regime is observed after a fast decay transient. For α ≪ 1 a transient exponential regime is observed, over which the theoretical predictions by George and Wang (Phys Fluids 21(2):025108, 2009) are satisfied. This transient regime lasts longer for smaller α values. A power law decay follows the exponential transient. The magnitude of the power law exponent in this case is significantly higher than the classical value derived in the case of free HIT decay and is determined by the time evolution law of F(k, t). In the last case, which is for α ≈ 1, the physical quantities show a different sensitivity to the parameter investigated. A number of anomalous results are observed, such as a time evolution of the turbulence coefficient C _ɛ .